1/1.2+1/3.4 +...+1/49.50):(30/26+31/27+...+54/50-25)
mik ko bt nhắn kiểu p/số, thông cảm
K
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K
0
TA
2
LV
4 tháng 4 2016
\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}\)
=>\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}\)
=>\(A=1-\frac{1}{50}=\frac{49}{50}\)
mà A=49/50
=>1/26+1/27+...+1/50 =49/50
DH
1
DN
0
P
2
TT
5 tháng 2 2020
Ta có : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{25}\right)\)
\(=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\)
Khi đó : \(\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right):\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\)
\(=\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right):\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right)=1\) (đpcm)
XO
5 tháng 2 2020
Ta có : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
= \(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
= \(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+...+\frac{1}{25}\right)=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\)
Khi đó \(\frac{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}{\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}}=\frac{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}=1\left(\text{đpcm}\right)\)
NT
0
PH
2
FF
24 tháng 8 2016
ta có:
1/1.2+1/3.4+1/5.6+...+1/49.50
=>1-1/2+1/3-1/4+1/5-1/6+...+1/49-1/50
=>(1+1/3+1/5+1/7+...+1/49)-(1/2+1/4+1/6+...+1/50)
=>(1+1/2+1/3+...+1/49+1/50)-(1/2+1/4+1/6+...+1/50).2
=>(1+1/2+1/3+...+1/49+1/50) -( 1+1/2+1/3+...+1/25)
=>1/26+1/27+1/28+...+1/50=1/26+1/27+1/28+...+1/50
hay 1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+1/28+...+1/50
